A pilot of mass m in a jet aircraft executes a\"loop-the-loop\" maneuver as illu

Question

A pilot of mass m in a jet aircraft executes a"loop-the-loop" maneuver as illustrated in Figure 5.14a. Theaircraft moves in a vertical circle of radius 2.68 km at aconstantspeed of 240 m/s.
a. Calculatethe force on the pilot causing the centripetal acceleration if theaircraft is midway up the loop as in Figure 5.14a. Express youranswer in units of mg.
a. Calculatethe force on the pilot causing the centripetal acceleration if theaircraft is midway up the loop as in Figure 5.14a. Express youranswer in units of mg.

Explanation / Answer

radius r= 2.68 km = 2680 m speed v = 240 m / s force at any point is F = mg cos + ( mv ^ 2 / r) At midway = 90 degrees So, force F = mg cos 90 + ( mv ^ 2 / r )                  = mg * 0+ m [ 240 ^ 2 / 2680 ]                  = 21.49 m                  = ( 21.49 m / 9.8 ) * 9.8                  = ( 2.193 m ) g Since g = 9.8 m / s ^ 2                  = 2.193 mg

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